頁籤選單縮合
題名 | On Deconvolution Using Time of Flight Information in Positron Emission Tomography |
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作者 | Zhang,Hang Paul; | 書刊名 | Statistica Sinica |
卷期 | 2:2 1992.07[民81.07] |
頁次 | 頁553-575 |
分類號 | 414.93 |
關鍵詞 | 正子電腦斷層造影術; Density estimation; Deconvoluting kernel estimator; Minimax; Radon transform; Tomography; |
語文 | 英文(English) |
英文摘要 | We study an estimation problem is PET when the time-of-flight information is available. The continuous idealization of the PET reconstruction problem, formulated by Johnstone and Silverman (1990) as a special case of bivariate density estimation based on indirect observations, is used. A Modified Deconvoluting Kernel Density Estimator (MDK) is proposed. For densities with mth derivatives satisfying α Lipschitz condition in □ norm and in □ norm, the convergence rates of mean integrated square error and maximum mean square error are shown to be □ where n is the number of counts. These rates are optimal. By comparing our results with those in the literature where time-of-flight is considered, it is shown that although the time of flight does not yield better convergence rates in this model, it can yield better constants when the noise is small. |
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